Is Dragos rule evidence of hybridization theory's failure?

[Hamiltonian]

TL;DR

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Drago rule states that if –

1. the central atom has at least one lone pair of electron on it
2. the central atom belongs to group 13,14,15 or 16 and is from the 3rd to 7th period.
3. if electronegativity of the central element is 2.5 or less
4. no. of sigma bonds+ lone pair=4

then, there is no need to consider the Hybridization of that element.

Drago's rule was introduced to explain why the bond angles of molecules such as $PH_3$, $AsH_3$, $SbH_3$ differ so much from $109^o28'$ which is supposed to be the ideal bond angle of molecules with $sp^3$ hybridization(as the steric number $Z = 4$). Is the fact that Dragos rule exists prove somewhat the failure of hybridization theory as the theory itself predicts the bond angles to be $109^o28'$ but in actuality, the bond angles are closer to $90^o$ hence implying hybridization does not take place?

The theory of hybridization does not account for the bond angles of these elements to be ($\approx 90^o$) and Dragos rule was born out of only experimental data.
The only theoretical proof that I have found that predicts Dragos rule is

(https://madoverchemistry.com/2018/1...l-bonding-24-covalent-bonding23-drago-rule-2/)
I am unclear as to how they get those equations(I can't find post 69 but I suspect its an equation from orbital analysis but I am not too sure) here it is proving by contradiction that no hybridization is going to take place in phosphine($PH_3$) instead of solely relying on experimental data.

so in short I don't understand:
1. the theoretical prediction of Dragos rule(which is given in the link above) using orbital analysis.
2. If the fact that Dragos rule exists proves the failure of hybridization theory.

 

[Borek]

If I understand correctly what is happening here is this:

1. There exists a general theory (call it Q) allowing us to describe electrons in any molecule.
2. This theory is way too inconvenient for everyday use, so we devised a simplified theory O, based on Q.
3. O is simplified, so it doesn't account for some phenomena we observe in reality, thus we add another theory, H, that helps us describe them.
4. Because of these simplifications O with H still fail, so we add an experimental rule D, to predict when H stops working.

Now you are trying to find a rationale behind O, H and D, that will allow you to treat them the same way we treat Q. Well - it won't work, because O and H are just simplified attempts at explaining the more complicated reality. In a way there is no need to prove they are wrong, as they are wrong by design. They do share many characteristics of the full theory Q, but they also ignore some details, so by definition now and then they have to fail.

 

[Hamiltonian]

If I understand correctly what is happening here is this:

1. There exists a general theory (call it Q) allowing us to describe electrons in any molecule.
2. This theory is way too inconvenient for everyday use, so we devised a simplified theory O, based on Q.
3. O is simplified, so it doesn't account for some phenomena we observe in reality, thus we add another theory, H, that helps us describe them.
4. Because of these simplifications O with H still fail, so we add an experimental rule D, to predict when H stops working.

Now you are trying to find a rationale behind O, H and D, that will allow you to treat them the same way we treat Q. Well - it won't work, because O and H are just simplified attempts at explaining the more complicated reality. In a way there is no need to prove they are wrong, as they are wrong by design. They do share many characteristics of the full theory Q, but they also ignore some details, so by definition now and then they have to fail.

just out of curiosity what would theory Q be (molecular orbital theory?)
also, I still don't understand the equations in the post above that predict the %s character.

 

[Borek]

Broadly speaking Q is the quantum theory based on the Schrödinger equation H\Psi=E\Psi.

Note that the notion of orbitals (O) is a simplification. Schrödinger equation describes the system (atom, molecules) as a whole, and its solution doesn't treat every electron individually. Assigning electrons to orbitals and finding solutions in terms of these orbitals makes math easier and results much more palatable, but in general it is only an approximation. In many cases a very good one, but not always - that's why we need tricks like hybridization. MO is another variant of a simplified theory - similar to O, just applied to larger systems.

 

[Hamiltonian]

Broadly speaking Q is the quantum theory based on the Schrödinger equation H\Psi=E\Psi.

Note that the notion of orbitals (O) is a simplification. Schrödinger equation describes the system (atom, molecules) as a whole, and its solution doesn't treat every electron individually.

what does its solution yield? ( the shape of the atom in 3d space?)

assigning electrons to orbitals and finding solutions in terms of these orbitals makes math easier and results much more palatable, but in general it is only an approximation. In many cases a very good one, but not always - that's why we need tricks like hybridization. MO is another variant of a simplified theory - similar to O, just applied to larger systems.

I think I don't know enough math to truly understand this:(

 

[Borek]

what does its solution yield? ( the shape of the atom in 3d space?)

Wave function Ψ and energy E. Squared wave function is an electron density, so it is related to the shape.

I think I don't know enough math to truly understand this:(

Don't worry, just remember, that this is a wast subject and things you are taught now are just simplified approaches. On many levels they are good enough, but they will be never fully consistent.

 

[DrDu]

Strangely enough, for at least 50 years now, no theoretical chemist believes any more in the geometry being dictated by hybridization. Yet teachers don't stop parroting this old lore.

 

[Hamiltonian]

Strangely enough, for at least 50 years now, no theoretical chemist believes any more in the geometry being dictated by hybridization.

probably because they know of a much more elegant theory(the Schrödinger equation as mentioned above) that doesn't need a whole lot of exceptions like hybridization and molecular orbital theory.

 

[DrClaude]

Strangely enough, for at least 50 years now, no theoretical chemist believes any more in the geometry being dictated by hybridization. Yet teachers don't stop parroting this old lore.

Are there general rules that have replaced hybridization? What would be the better way to teach this?

(In case my questions may sound negative, they are not. I am genuinely interesting in figuring out how to best teach this.)

 

[DrDu]

On a simple level, VSEPR theory comes to my mind.